Different with the plain flexible job-shop scheduling problem (FJSP), the FJSP with routing flexibility is more complex and it can be deemed as the integrated process planning and (job shop) scheduling (IPPS) problem, where the process planning and the job shop scheduling two important functions are considered as a whole and optimized simultaneously to utilize the flexibility in a flexible manufacturing system. Although, many novel meta-heuristics have been introduced to address this problem and corresponding fruitful results have been observed; the dilemma in real-life applications of resultant scheduling schemes stems from the uncertainty or the nondeterminacy in processing times, since the uncertainty in processing times will disturb the predefined scheduling scheme by influencing unfinished operations. As a result, the performance of the manufacturing system will also be deteriorated. Nevertheless, research on such issue has seldom been considered before. This research focuses on the modeling and optimization method of the IPPS problem with uncertain processing times. The neutrosophic set is first introduced to model uncertain processing times. Due to the complexity in the math model, we developed an improved teaching-learning-based optimization(TLBO) algorithm to capture more robust scheduling schemes. In the proposed optimization method, the score values of the uncertain completion times on each machine are compared and optimized to obtain the most promising solution. Distinct levels of fluctuations or uncertainties on processing times are defined in testing the well-known Kim’s benchmark instances. The performance of computational results is analyzed and competitive solutions with smaller score values are obtained. Computational results show that more robust scheduling schemes with corresponding neutrosophic Gantt charts can be obtained; in general, the results of the improved TLBO algorithm suggested in this research are better than those of other algorithms with smaller score function values. The proposed method in this research gives ideas or clues for scheduling problems with uncertain processing times.

与普通的灵活作业车间调度问题（FJSP）不同，具有路由灵活性的 FJSP 更复杂，可以看作是集成工艺计划和（作业车间）调度（IPPS）问题，其中工艺计划和作业车间调度两个重要功能被视为一个整体并同时优化以利用柔性制造系统中的灵活性。尽管已经引入了许多新颖的元启发式来解决这个问题，并且已经观察到了相应的富有成效的结果；结果调度方案在实际应用中的困境源于处理时间的不确定性或不确定性，因为处理时间的不确定性会通过影响未完成的操作来干扰预定的调度方案。因此，制造系统的性能也将恶化。然而，以前很少考虑对此类问题的研究。本研究侧重于处理时间不确定的 IPPS 问题的建模和优化方法。中智集首先被引入来模拟不确定的处理时间。由于数学模型的复杂性，我们开发了一种改进的基于教学的优化 (TLBO) 算法来捕获更强大的调度方案。在所提出的优化方法中，对每台机器上不确定完成时间的得分值进行比较和优化，以获得最有希望的解决方案。在测试著名的 Kim 基准实例时，定义了不同级别的处理时间波动或不确定性。分析计算结果的性能，并获得具有较小分值的竞争解决方案。计算结果表明，可以获得具有相应中智甘特图的更鲁棒的调度方案；总的来说，本研究提出的改进TLBO算法的结果优于其他具有较小分数函数值的算法。本研究中提出的方法为处理时间不确定的调度问题提供了思路或线索。本研究提出的改进 TLBO 算法的结果优于其他具有较小分数函数值的算法。本研究中提出的方法为处理时间不确定的调度问题提供了思路或线索。本研究中提出的改进的 TLBO 算法的结果优于其他具有较小分数函数值的算法。本研究中提出的方法为处理时间不确定的调度问题提供了思路或线索。